- Governing equations - Navier-Stokes
-
- Growth rate \(\Psi(x, z, t) = Ae^{-\alpha|z|}\exp\left[i\alpha(x-ct)\right]\)
- Assumptions - fluid behaviour of 2 layers with a perturbed interface, etc. Applies equally to layers of gases, liquids, or viscous solids.
- Basic scalings - density contrast and wavelength per unit thickness
- Review papers that have applied these equations to the lithosphere (e.g., \citealp*{Conrad1997}).
- Result - drips are expected to be 100 km in wavelength, but could be larger if background strain rate (shortening) is high
- Limitations (which leads into models) - boundary conditions, complicated rheologies
Other modes of foundering
- Foundering of a dense root: It's similar to RTI but doesn't fit the simple scheme above. Instead of 2 layers with an interface, there is a third body imposed within or between the layers.
- Weakening by fluids or melt and breaking off? (Northern Andean volcanic zone)
- Ablative removal, thermal erosion, shear entrainment, subduction removal, ... ?
Models - keep it brief
- Commonalities, setups, equations (Stokes), solvers, etc.
- Differences
- Insights: dripping itself, surface deformation, melting/volcanism, geochem (?)
- 2d vs 3d: future models should be 3d
Synthesis
- Scale of RTI should be ~100 km, larger if b/g strain rate is high
- Scale of other modes: smaller for weakened foundering, larger for root removal?
- Time scales?
- Volcanism and sources of melt - melting of drips possible
- Can we distinguish between RTI, weakened foundering, and root removal? If so, that would be a major part of the rest of the paper.
Analysis: Locations of foundering
North America
- Transverse ranges - first
- Southern SN (Isabella) - most papers, most data. Also northern SN (Redding)
- Wallowa mountains
- Central NV
- Grand Canyon
- Others
- Alternative hypothesis - fossil slabs
South America
Pamir-Himalaya-Tibet
- Pamir - Vanj and Dunkeldik
- Himalaya
- Tibet
Other
- SE Carpathians?
- New Zealand
Synthesis